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Sparse bounds for discrete singular Radon transforms

Volume 165 / 2021

Theresa C. Anderson, Bingyang Hu, Joris Roos Colloquium Mathematicum 165 (2021), 199-217 MSC: Primary 42B20; Secondary 42B15. DOI: 10.4064/cm8296-8-2020 Published online: 21 December 2020

Abstract

We show that discrete singular Radon transforms along a certain class of polynomial mappings $P:\mathbb {Z}^d\to \mathbb {Z}^n$ satisfy sparse bounds. For $n=d=1$ we can handle all polynomials. In higher dimensions, we pose restrictions on the admissible polynomial mappings stemming from a combination of interacting geometric, analytic and number-theoretic obstacles.

Authors

  • Theresa C. AndersonPurdue University
    150 N University St.
    West Lafayette, IN 47907, U.S.A.
    e-mail
  • Bingyang HuPurdue University
    150 N University St.
    West Lafayette, IN 47907, U.S.A.
    e-mail
  • Joris RoosUniversity of Massachusetts Lowell
    220 Pawtucket St.
    Lowell, MA 01854, U.S.A.
    e-mail

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